CN111093865B

CN111093865B - Method and apparatus for analyzing layered structure, method and apparatus for manufacturing layered structure

Info

Publication number: CN111093865B
Application number: CN201880058266.8A
Authority: CN
Inventors: 柴原正和; 生岛一树; 河原充; 竹内梨乃; 桥诘光
Original assignee: Public University Legal Person Osaka
Current assignee: Public University Legal Person Osaka
Priority date: 2017-09-08
Filing date: 2018-09-07
Publication date: 2022-03-08
Anticipated expiration: 2038-09-07
Also published as: US20200331102A1; CN111093865A; JP7125764B2; WO2019049981A1; JPWO2019049981A1

Abstract

The displacement and stress calculation unit (220) is configured to calculate the residual stress and the deformation by performing a thermo-elastic-plastic analysis using an idealized explicit solution FEM. The magnitude of the temperature increase is set to a value larger than the magnitude of the temperature increase used in the thermo-elasto-plastic analysis by the static implicit solution FEM. Each of the plurality of blocks is heated in a heating mode in which the plurality of blocks that are not adjacent to each other are simultaneously heated. Heating of each block is performed by a surface heat source having a heat supply amount adjusted with respect to a heat supply amount in the case of heating by a moving heat source.

Description

Method and apparatus for analyzing layered structure, method and apparatus for manufacturing layered structure

Technical Field

The present disclosure relates to a method and an apparatus for analyzing a layered structure, and a method and an apparatus for manufacturing a layered structure.

Background

In recent years, attention has been paid to a layered shaped article produced by solidifying and accumulating a molten material. For example, a so-called metal 3D printer is known which forms an object of a desired shape by irradiating a metal powder with a laser beam, an electron beam, or the like to melt and solidify the metal powder. Japanese patent No. 2620353 discloses a method of: a three-dimensional shaped layered structure is produced by irradiating a predetermined position of a powder layer of metal or the like with a laser beam to sinter the powder at the position to form a sintered layer, and sequentially forming such sintered layers.

In addition, a laminate molding using resin powder, a laminate molding in which molten resin or metal melted by arc discharge is deposited, and the like are known.

Documents of the prior art

Patent document

Patent document 1: japanese patent No. 2620353

Disclosure of Invention

Problems to be solved by the invention

For example, in the laminate molding using a metal 3D printer, since an object is produced while a metal powder is melted and solidified by irradiating the metal powder with a laser beam, an electron beam, or the like, an extremely large residual stress and deformation may occur in the produced laminate molded object. Such residual stress and deformation cause problems such as poor dimensional accuracy and cracking of the resulting layered structure.

Therefore, it is sometimes necessary to previously investigate residual stress and deformation generated in the layered structure before the layered structure is formed. However, the residual stress is difficult to measure by studies using experiments with real objects, and may cause a problem in terms of cost.

Therefore, it is desirable to analyze residual stress and deformation generated in the layered structure by a computer in advance. If the residual stress and the distortion generated in the layered shaped article can be analyzed and predicted by a computer, the influence of each factor such as the stress and the distortion generated in the layered shaped article can be easily studied, and the number of trial-production of the product can be reduced to reduce the cost.

In the analysis of such residual stress and deformation by a computer, a thermo-elasto-plastic analysis using a finite Element method (fem) is useful. However, in the static implicit solution FEM generally used in such a thermo-elastic-plastic analysis, it is necessary to successively solve the rigid equation (multiple primary simultaneous equations) of the entire system in each calculation step, and therefore it is practically difficult to apply the static implicit solution FEM to a particularly large-scale modeling analysis from the viewpoint of calculation time.

Therefore, an object of the present disclosure is to significantly reduce the calculation time in an analysis method and an analysis apparatus for analyzing residual stress and deformation generated in a layered shaped object by a computer.

Another object of the present disclosure is to provide a method and an apparatus for manufacturing a layered shaped article, which can suppress residual stress and deformation generated in the layered shaped article.

Means for solving the problems

The method for analyzing a layered shaped object according to the present disclosure is a method for analyzing a residual stress and deformation generated in a layered shaped object by a computer, the layered shaped object being generated by solidifying and continuously stacking a molten material, the method comprising the steps of: inputting data for performing a thermo-elasto-plastic analysis of a laminated shaped object using a FEM; and calculating residual stress and deformation occurring in the layered shaped object by performing thermo-elastic-plastic analysis in accordance with time-series data of a temperature distribution generated in the layered shaped object accompanying the shaping of the layered shaped object. In the step of calculating the residual stress and the distortion, when the temperature increase according to the time-series data is provided, the displacement and the stress of the layered structure are calculated by the dynamic explicit solution FEM until the predetermined static equilibrium condition is reached, and when the displacement reaches the static equilibrium condition, the temperature increase is provided again, and the displacement and the stress are calculated again. Here, the magnitude of the temperature increase is set to a value larger than the magnitude of the temperature increase used in the thermo-elasto-plastic analysis of the layered structure by the static implicit solution FEM. The heating of the layered structure is performed by using an instantaneous surface heat source having a heat supply amount adjusted with respect to a heat supply amount in the case of heating by the moving heat source.

The device for analyzing a layered shaped object according to the present disclosure analyzes residual stress and deformation generated in the layered shaped object by solidifying a molten material on a surface layer, and includes an input unit and a calculation unit. The input unit is configured to input data for performing a thermo-elastic-plastic analysis of the layered structure using the FEM. The calculation unit is configured to calculate residual stress and distortion generated in the layered shaped object by performing thermo-elastic-plastic analysis in accordance with time-series data of a temperature distribution generated in the layered shaped object in accordance with the shaping of the layered shaped object. When the temperature increment according to the time-series data is provided, the calculation unit calculates the displacement and stress of the layered structure by using the dynamic explicit solution FEM until a predetermined static equilibrium condition is reached, and when the displacement reaches the static equilibrium condition, the calculation unit provides the temperature increment again and calculates the displacement and stress again. Here, the magnitude of the temperature increase is set to a value larger than the magnitude of the temperature increase used in the thermo-elasto-plastic analysis of the layered structure by the static implicit solution FEM. The heating of the layered structure is performed by using an instantaneous surface heat source having a heat supply amount adjusted with respect to a heat supply amount in the case of heating by the moving heat source.

In the above-described method and apparatus for analyzing a layered structure, when a temperature increase is given in accordance with time-series data, the displacement and stress of the layered structure are calculated by the dynamic explicit solution FEM until a predetermined static equilibrium condition is reached, and when the displacement reaches the static equilibrium condition, the temperature increase is given again and the displacement and stress are calculated again (idealized explicit solution FEM). According to such an idealized explicit solution FEM, since the solution converges even if a large temperature increase is provided, the present analysis method and analysis apparatus are provided with a large temperature increase (large temperature increase) compared with the size of the temperature increase used in the thermo-elasto-plastic analysis using the static implicit solution FEM. This can reduce the number of calculations and shorten the calculation time. In addition, in the present analysis method and analysis device, the heating of the layered shaped object is performed by using the instantaneous surface heat source after the amount of heat supplied is adjusted, and therefore, this can also shorten the calculation time (instantaneous heat source model). Therefore, according to the method and the apparatus for analyzing a layered structure of the present disclosure, the calculation time can be significantly shortened.

Preferably, the heating of the layered shaped article is performed for each of the uppermost layers of the plurality of divided blocks of the layered shaped article. The heating of each block is performed by using the above-described instantaneous surface heat source.

More preferably, the heating for the layered molding is performed in a heating mode in which at least two blocks that are not adjacent to each other are simultaneously heated.

Thus, since heating is performed for each of the plurality of blocks, the calculation time (simultaneous heating mode) can be further shortened.

Preferably, the amount of heat supplied by the instantaneous surface heat source is adjusted relative to the amount of heat supplied when heating is performed by the moving heat source such that the amount of shrinkage of the layered shaped article is equal to the amount of shrinkage of the layered shaped article when heating is performed by the moving heat source.

Preferably, the material is a metal and the magnitude of the temperature increase is at least 100 degrees or more.

Preferably, the magnitude of the temperature increase is determined based on the mechanical melting temperature of the metal constituting the layered structure.

Further, a method for manufacturing a layered shaped article according to the present disclosure is a method for manufacturing a layered shaped article that is generated by solidifying and continuously accumulating molten materials, and includes: determining a heating pattern when heating the uppermost layer of the layered structure based on the analysis result obtained by the analysis method; and heating the layered shaped object in accordance with the heating pattern.

Further, a device for manufacturing a layered shaped article according to the present disclosure is a device for manufacturing a layered shaped article that is generated by solidifying and continuously accumulating molten materials, and includes: a heating device configured to heat an uppermost layer of the layered structure; and a control device configured to control the heating device. The control device determines a heating pattern when heating the uppermost layer of the layered shaped object based on the analysis result obtained by the analysis method, and controls the heating device so that heating of the layered shaped object is performed in accordance with the heating pattern.

According to the above-described manufacturing method and manufacturing apparatus, a heating pattern capable of suppressing residual stress and distortion is determined based on the analysis result obtained by the above-described analysis method, and the layered shaped article can be manufactured according to the heating pattern.

The method of manufacturing a layered shaped article according to the present disclosure is also a method of manufacturing a layered shaped article that is generated by solidifying and continuously accumulating molten materials. The heating of the layered shaped article is performed for each of the uppermost layers of the plurality of blocks into which the layered shaped article is divided. Further, the manufacturing method includes the steps of: heating the peripheral-most block; and heating the block on the inner peripheral side of the block on the most peripheral portion after heating the block on the most peripheral portion.

Further, a device for manufacturing a layered shaped article according to the present disclosure is a device for manufacturing a layered shaped article that is generated by solidifying and continuously accumulating molten materials, and includes: a heating device configured to heat an uppermost layer of the layered structure; and a control device configured to control the heating device to heat each of the uppermost blocks divided into the plurality of blocks. The control device is configured to heat the block on the inner peripheral side of the block on the outermost peripheral edge portion after heating the block on the outermost peripheral edge portion by controlling the heating device.

According to the manufacturing method and the manufacturing apparatus described above, the residual stress generated in the outermost peripheral edge portion of the layered shaped article can be suppressed.

ADVANTAGEOUS EFFECTS OF INVENTION

According to the method and the apparatus for analyzing a layered structure of the present disclosure, the calculation time can be significantly shortened.

Further, according to the method and apparatus for manufacturing a layered shaped article of the present disclosure, residual stress generated in the layered shaped article can be suppressed.

Drawings

Fig. 1 is a diagram showing an analysis model of a metal layered structure as an example of a layered structure analyzed by an analysis method according to an embodiment of the present disclosure.

Fig. 2 is a diagram showing elements of an analysis model.

Fig. 3 is a diagram illustrating an example of a method for producing a metal layered structure by a metal 3D printer.

Fig. 4 is a diagram showing a case where the surface layer is molded by a laser melting method.

Fig. 5 is a diagram conceptually illustrating a thermo-elasto-plastic analysis of FEM using an idealized explicit solver.

Fig. 6 is a plan view of the analysis model shown in fig. 1.

Fig. 7 is a diagram showing a case where each block is heated by a moving heat source as a comparative example.

Fig. 8 is a diagram showing a case where each block is heated by the instant surface heat source.

Fig. 9 is a block diagram showing a main part of the hardware configuration of the analysis device according to the present embodiment.

Fig. 10 is a functional block diagram showing the configuration of the analysis device shown in fig. 9 in terms of functions.

Fig. 11 is a flowchart for explaining a processing procedure of FEM thermo-elasto-plastic analysis performed by the analysis apparatus shown in fig. 9.

Fig. 12 is a graph showing the shrinkage of the analysis target when the temperature increase is changed.

Fig. 13 is a diagram showing the shrinkage of the analysis target in the case of using the instantaneous heat source model.

Fig. 14 is a flowchart for explaining a processing procedure of FEM thermo-elastic-plastic analysis performed by the analysis apparatus in the modification.

Fig. 15 is a diagram schematically showing a configuration of a metal 3D printer shown as an example of a manufacturing apparatus for a layered shaped object.

Fig. 16 is a first diagram illustrating an example of a heating procedure for a plurality of blocks.

Fig. 17 is a second diagram illustrating an example of a heating procedure for a plurality of blocks.

Fig. 18 is a first diagram showing an example of the analysis result of the residual stress generated in the layered structure.

Fig. 19 is a second diagram showing an example of the analysis result of the residual stress generated in the layered structure.

Fig. 20 is a flowchart illustrating an example of a procedure of processing executed by the controller.

Detailed Description

Embodiments of the present disclosure are described below in detail with reference to the drawings. In the drawings, the same or corresponding portions are denoted by the same reference numerals, and description thereof will not be repeated.

Fig. 1 is a diagram showing an analysis model of a metal layered structure as an example of a layered structure analyzed by an analysis method according to an embodiment of the present disclosure. Although fig. 1 shows a simple model of a rectangular structure as an example, the model that can be analyzed by the present analysis method is not limited to the model of the structure shown in fig. 1.

Referring to fig. 1, the analysis model 10 is obtained by modeling a metal-laminated shaped object (analysis target) laminated and shaped on a base plate 12 by a metal 3D printer (not shown). In this example, the analysis model 10 is set to have a size of 30mm × 30mm × 1.2 mm. As shown in fig. 2, the size of each element constituting the analysis model 10 is set to 0.1mm × 0.1mm × 0.03mm in accordance with the size of laser light (described later) irradiated at the time of the lamination molding. Therefore, the number of elements of the analysis model 10 is 360 ten thousand, and the number of layers is 40.

Fig. 3 is a diagram illustrating an example of a method for producing a metal layered structure by a metal 3D printer. In fig. 3, a laser melting method in which a metal powder of a material is melted by irradiating the metal powder with a laser beam is shown, but an electron beam melting method in which a metal powder is melted by irradiating a metal powder with an electron beam can also be applied to the analysis method of the present disclosure.

In addition, although fig. 3 shows an SLM (Selective Laser Melting) method in which a powder bed of Metal powder filled with a material is selectively irradiated with Laser light to perform lamination molding, an LMD (Laser Metal Deposition) method in which Laser light and Metal powder are simultaneously irradiated to perform lamination molding may be applied to the analysis method of the present disclosure.

Referring to fig. 3, the elevator 20 for placing the intermediate shaped object 24 and the metal powder 22, which are produced in step IV described later, is lowered by one layer thickness (step I). Next, the metal powder 26 is supplied onto the intermediate shaped object 24 and the metal powder 22 in an amount corresponding to the next layer (step II). Next, the metal powder 26 is homogenized by the knife roll 28 (step III). After the forming region is preheated, the metal powder 26 is selectively melted and solidified (sintered) using the laser light 32 output from the torch 30 as a heat source, thereby forming a surface layer (step IV). By repeating such a series of steps I to IV, the metal layer is formed into a desired metal layered structure.

Fig. 4 is a diagram showing a case where the surface layer is molded by a laser melting method. Referring to fig. 4, the torch 30 is moved while the laser beam 32 is irradiated to the metal powder 26 newly supplied to the solidified intermediate shaped object 24. The metal powder 26 irradiated with the laser light 32 forms a molten pool 34 and melts the surface of the underlying intermediate shaped object 24, thereby forming a new layer 36 joined to a heat affected zone 38 formed in the surface layer of the intermediate shaped object 24.

Although not particularly shown, the laser beam 32 may be similarly shaped by an electron beam melting method of irradiating an electron beam.

Referring again to fig. 1, in the present embodiment, the analysis model 10 is subjected to thermo-elasto-plastic analysis using FEM. Accordingly, the residual stress and the distortion generated in the metal laminated shaped object to be analyzed by the analysis model 10 can be predicted by the computer, so that the influence of each factor such as the stress and the distortion generated in the laminated shaped object can be easily studied, and the number of trial-production of the product can be reduced to reduce the cost.

However, in the static implicit solution FEM generally used in such a thermo-elastic-plastic analysis, it is necessary to successively solve the rigidity equation (multiple primary simultaneous equations) of the entire system in each calculation step, and therefore it is practically difficult to apply the static implicit solution FEM to the modeling analysis of the metal laminated modeled object in a large scale as shown in fig. 1 from the viewpoint of calculation time.

Therefore, in the analysis method according to the present embodiment, it is not necessary to solve simultaneous equations in each calculation step as in the static implicit solution FEM, and the analysis model 10 is subjected to the thermo-elasto-plastic analysis by the "idealized explicit solution FEM" capable of analyzing the residual stress and deformation of a large-scale structure. Further, according to the idealized explicit solution FEM, since the solution converges even if the temperature increase (which is a temperature step at the time of calculation and takes a negative value during cooling) is increased, the analysis method according to the present embodiment can provide a large temperature increase size (for example, 100 degrees or more) (a large temperature increase) compared to the temperature increase size (generally, a temperature increase of 15 degrees or 30 degrees) used in the thermo-elasto-plastic analysis by the static implicit solution FEM. This reduces the number of calculations required to perform the analysis, and shortens the calculation time.

In the analysis method according to the present embodiment, the model for heating the analysis model 10 is a model (instantaneous heat source model) heated by an instantaneous surface heat source having a heat supply amount adjusted with respect to the heat supply amount in the case of heating by a moving heat source that moves the laser light 32 at a predetermined speed and heats the laser light.

The model for heating the analysis model 10 may be a model for heating a plurality of blocks in a random order in a heating mode for simultaneously heating at least two blocks that are not adjacent to each other (simultaneous heating mode). The "simultaneous" may not be completely simultaneous as long as it is substantially simultaneous. The heating sequence does not necessarily have to be random, but may be regular. In the analysis method according to the present embodiment, heating is performed in the simultaneous heating mode, and each block is heated by an instantaneous surface heat source using an instantaneous heat source model. This can significantly reduce the calculation time required for analysis.

As described above, according to the analysis method of the present embodiment, the calculation time required for analysis can be significantly reduced by using the "large temperature increase" and the "instantaneous heat source model" as described above and also using the "simultaneous heating mode".

First, a thermal elastoplasticity analysis by an idealized explicit solution FEM will be briefly described, and "large temperature increase", "simultaneous heating mode", and "instantaneous heat source model" which are features of the present embodiment will be described in detail.

< thermo-elastoplasticity analysis by idealized explicit solution FEM >

Fig. 5 is a diagram conceptually illustrating a thermo-elasto-plastic analysis of FEM using an idealized explicit solver. Referring to fig. 5, thermo-elasto-plastic analysis using an idealized explicit solution FEM was performed as follows.

When the node displacement vector at time t is set as { u }_tThe equilibrium equation used in the idealized explicit solver FEM is expressed by the following equation (1).

[ number 1]

Here, [ M ] M]Represents a quality matrix, [ C ]]Represents a damping matrix, [ K ]]Denotes a rigid matrix, { F }_tRepresenting the load vector. In addition, the quality matrix [ M ]]And a damping matrix [ C ]]Is a matrix adjusted to a node-concentrated diagonal matrix.

In the thermo-elasto-plastic analysis, when time-series data of a temperature distribution of an analysis target (in the present embodiment, the analysis model 10) is supplied as input data, in the idealized explicit solution FEM, the time-series data of the temperature distribution is calculated by a thermal conductivity analysis described later, and a load generated from a temperature increase based on the time-series data of the temperature distribution is supplied as a load vector of expression (1) (load step (1) in fig. 5).

Then, the displacement (curve k1) in the load step (temperature step) is obtained by solving the above equation (1) for the load step (temperature step). Specifically, the equation (1) is solved for each virtual time step by the dynamic explicit solution FEM to obtain the displacement, and the calculation of the displacement is repeated until the displacement reaches the static equilibrium state, that is, until the influence of the inertia term and the damping term in the equation (1) is reduced to a negligible degree and the displacement converges to a value equivalent to the solution obtained by the static implicit solution FEM ((2) in fig. 5).

When the displacement reaches the static equilibrium state (3) in fig. 5), the load step (temperature step) (fig. 5 ((4)) is advanced. Then, the displacement in the load step (temperature step) is obtained (curve k2), and calculation is repeated by the dynamic explicit solution FEM until the displacement reaches the static equilibrium state ((5) in fig. 5).

According to the idealized explicit solution FEM, since analysis is performed by dividing the calculation into virtual time steps, the number of calculation steps itself increases, but it is not necessary to solve simultaneous equations for each step as in the case of the static implicit solution FEM. Thus, the computation in each computation step is much less than that of the static implicit solution FEM. In addition, since the convergence calculation is performed in each load step (temperature step) to satisfy the static equilibrium condition, the analysis accuracy is better than that of the method using only the dynamic explicit solution FEM.

< description of Large temperature increment >

According to the idealized explicit solution FEM described above, the solution converges even if the temperature step (load step) is increased. Therefore, in the analysis method according to the present embodiment, a large temperature step (large temperature increase) is provided compared with the temperature step used in the thermo-elasto-plastic analysis using the static implicit method FEM. In general, when the solution does not converge and a small temperature step (temperature increase) of about 15 degrees or 30 degrees is required to be suppressed if the temperature step is increased in the thermo-elasto-plastic analysis by the static implicit solution FEM, the analysis method according to the present embodiment can provide a load step corresponding to a temperature step (temperature increase) of 100 degrees or more. This reduces the number of calculations required to perform the analysis, and shortens the calculation time.

< description of simultaneous heating mode and instantaneous Heat Source model >

Fig. 6 is a plan view of the analytical model 10 shown in fig. 1. Referring to fig. 6, in the present embodiment, the uppermost layer (upper surface) of the analysis model 10 is divided into a plurality of blocks, and 4 blocks that are not adjacent to each other are simultaneously heated, thereby reducing the calculation time.

Specifically, in this example, the uppermost layer (the heating surface heated by the laser) of the analytical model 10 is divided into 4 regions a1 to a4, and each of the regions a1 to a4 is divided into 9 blocks B1 to B9. First, the blocks B1 in the respective regions a1 to a4 are heated simultaneously. Subsequently, the blocks B2 of the respective regions A1-A4 are simultaneously heated, and thereafter, the blocks Bi of the respective regions A1-A4 are sequentially and simultaneously heated. That is, in this example, 4 blocks Bi are heated simultaneously.

The heating sequence of each block in each region is performed in a random order. In the above, heating is performed in the order of B1 → B2 → · · · · but the heating order of the blocks is not limited thereto.

The method of dividing the region and block is not limited to the above method. In the above, each region is divided into 3 × 3 blocks as an example, but each region may not be divided into blocks, or each region may be divided into blocks of, for example, 5 × 5, 20 × 20, or the like. In these cases, the blocks are heated in each region in a random order.

As described above, "simultaneously" may not necessarily be completely simultaneously as long as they are substantially simultaneously. The heating sequence does not necessarily have to be random, but may be regular.

In addition, the blocks heated at the same time are determined not to be adjacent to each other to avoid residual stress remaining depending on the heating method. In the example shown in fig. 6, the heating order of the blocks B1-B9 is determined in each of the regions a1-a4 in such a manner that 4 blocks heated at the same time are not adjacent to each other.

In this example, the heating method of each block is performed by a surface heat source having a heat supply amount adjusted to the heat supply amount in the case of heating by the moving heat source.

Fig. 7 is a diagram showing a case where each block is heated by a moving heat source model as a comparative example, and fig. 8 is a diagram showing a case where each block is heated by an instantaneous heat source model (surface heat source). Referring to fig. 7, the moving heat source is a heat source according to an actual heating method, but since the heat source (torch 30 and laser 32) is moved and the elements are heated for each number of elements, the calculation time becomes long. In contrast, referring to fig. 8, in the instant heat source model, all elements in the uppermost layer of the block are heated simultaneously by the surface heat source 40. This can significantly shorten the calculation time. The surface heat source 40 can be said to be a heat source whose moving speed is infinitely large.

In the instant heat source model (surface heat source), since each of all the elements to be heated receives heat of the adjacent elements at the same time, when the same heat supply amount (J) as that of the moving heat source is supplied to the instant heat source model, the contraction amount of the shaped object tends to be larger than that in the case of the moving heat source due to the synergistic effect. Therefore, in the analysis method according to the present embodiment, the heating amount is adjusted with respect to the heating amount in the case of using the moving heat source (corresponding to actual heating) by using the following correction coefficient η 0.

Eta 0 ═ heat supply of instantaneous surface heat source)/(heat supply of mobile heat source) · (2)

As described above, in the analysis method according to the present embodiment, each of a plurality of blocks is heated in accordance with the simultaneous heating mode, and an instantaneous heat source model (surface heat source) is used in each block instead of a moving heat source. By adopting the large temperature increase described above and adopting such a heating model, the calculation time required for analysis can be significantly shortened.

< description of analysis System >

Fig. 9 is a block diagram showing a main part of the hardware configuration of the analysis device according to the present embodiment. Referring to fig. 9, the analyzer 100 includes an input Unit 110, an interface (I/F) Unit 120, a CPU (Central Processing Unit) 130, a RAM (Random Access Memory) 140, a ROM (Read Only Memory) 150, and an output Unit 160.

The CPU 130 implements the analysis method according to the present embodiment by executing various programs stored in the ROM 150. The RAM 140 is used as a work area by the CPU 130. The ROM 150 records a program including steps of a flowchart (described later) showing the procedure of the analysis method according to the present embodiment. The input unit 110 is a means for reading data from the outside, such as a keyboard, a mouse, a recording medium, and a communication device. The output unit 160 is a unit for outputting the calculation result of the CPU 130, such as a display, a recording medium, and a communication device.

Fig. 10 is a functional block diagram functionally illustrating the configuration of the analysis device 100 shown in fig. 9. Referring to fig. 10, the analyzer 100 includes a temperature distribution calculating unit 210, a displacement and stress calculating unit 220, a simplified calculation setting unit 230, and the input unit 110 and the output unit 160 described above.

Various data required for FEM thermal conductivity analysis (described later) performed by the temperature distribution calculation unit 210 are input from the input unit 110. As an example, data such as the shape/size of the analysis target (the analysis model 10 in the present embodiment), FEM element information, a heat source model, the temperature dependence of material constants (specific heat, density, heat conductivity, and the like), the temperature dependence of object surface characteristics (heat transfer coefficient), boundary conditions, and analysis conditions (time increment, initial temperature, interlayer temperature, type of element, and the like) are input.

Various data required for FEM thermo-elastic-plastic analysis performed by the displacement and stress calculation unit 220 are also input from the input unit 110. For example, in addition to the above data, data such as temperature dependence of material constants (young's modulus, yield stress, poisson's ratio, linear expansion coefficient, work hardening coefficient, and the like), selection of various models (hardening rule, yield condition, creep, phase transition, geometric linearity/nonlinearity, and the like), mechanical boundary conditions, geometric boundary conditions, and analysis conditions (types of elements, and the like) are input.

The temperature distribution calculation unit 210 calculates time-series data of the temperature distribution of the analysis target (analysis model 10) by performing FEM thermal conduction analysis using various data input from the input unit 110. In the FEM thermal conductivity analysis, various known thermal conductivity analysis methods using FEMs can be used.

The displacement and stress calculation unit 220 receives various data input from the input unit 110, and receives time-series data of the temperature distribution of the analysis target (analysis model 10) calculated by the temperature distribution calculation unit 210 from the temperature distribution calculation unit 210. The displacement and stress calculation unit 220 receives the temperature increase Δ T, the heating mode, and the settings of the heat source model, which are set in the simplified calculation setting unit 230, from the simplified calculation setting unit 230.

The simplified calculation setting unit 230 performs various settings for simplifying the calculation of the thermo-elastic-plastic analysis by the idealized explicit solution FEM performed by the displacement and stress calculation unit 220.

Specifically, the simplified calculation setting unit 230 sets the temperature increase Δ T in the calculation of the thermo-elastic-plastic analysis by the idealized explicit solution FEM. The magnitude of the temperature increase Δ T is set to a value larger than the magnitude of the temperature increase (typically 15 degrees or 30 degrees) used for calculation of the thermo-elasto-plastic analysis by the static implicit method FEM, and in the present embodiment, the simplified calculation setting unit 230 sets a predetermined temperature increase Δ T of 100 degrees or more.

The magnitude of the temperature increase Δ T may be determined based on the mechanical melting temperature of the metal constituting the metal laminated structure. For example, when the metal constituting the metal laminated shaped article is iron, the magnitude of the temperature increase Δ T may be set to a level of several hundreds of degrees based on the dynamic melting temperature of iron when the dynamic melting temperature of iron is about 750 to 800 degrees.

The simplified calculation setting unit 230 sets a heat supply mode in the thermo-elastic-plastic analysis calculation by the idealized explicit solution FEM. Specifically, as described in fig. 6, the simplified calculation setting unit 230 divides the uppermost layer (the heating surface heated by the laser) of the analysis model 10 into a plurality of areas a1-a4, and divides each area into a plurality of blocks B1-B9, and sets the heat supply mode so that 4 blocks Bi that are not adjacent to each other are simultaneously heated and are sequentially heated for each 4 blocks Bi.

The simplified calculation setting unit 230 sets a heat source model for the calculation of the thermo-elastic-plastic analysis by the idealized explicit solution FEM. Specifically, the simplified calculation setting unit 230 sets, as a heat source model for heating each block, an instantaneous heat source model (surface heat source) having a heat supply amount adjusted with respect to the heat supply amount in the case of heating by a moving heat source (corresponding to actual heating) using the correction coefficient η 0 represented by the above equation (2).

Then, the displacement and stress calculation unit 220 calculates time-series data of residual stress and displacement generated in the analysis target (analysis model 10) by performing FEM thermo-elastic analysis in accordance with the respective settings of the temperature increase Δ T, the heat supply mode, and the heat source model set in the simplified calculation setting unit 230, using the various data received from the input unit 110 and the time-series data of the temperature distribution of the analysis target (analysis model 10) received from the temperature distribution calculation unit 210.

The residual stress and the time-series data of the displacement calculated by the displacement and stress calculating unit 220 are output to the output unit 160. The output unit 160 may be a display for displaying time-series data of the calculated residual stress and displacement, a writing unit for writing the data in a predetermined format to a recording medium, a communication device for transmitting the data in a predetermined format to the outside, or the like.

Fig. 11 is a flowchart for explaining a processing procedure of FEM thermo-elasto-plastic analysis performed by the analysis apparatus 100 shown in fig. 9. Referring to fig. 11, the analysis device 100 calculates time-series data of the temperature distribution of the analysis target (analysis model 10) by performing FEM thermal conduction analysis (step S10). Next, the analysis device 100 sets an initial value 1 to the counter i (step S20). The counter i is used to select the block to be heated in the heating mode.

Next, the analysis device 100 updates the temperature field by considering that heat is applied from the instantaneous surface heat source to the i-th block of each of the areas a1-a4 (fig. 6) (temperature increase Δ T) (step S30). As described above, the temperature increase Δ T is set to be a large temperature increase and is a value (a predetermined value of 100 degrees or more) larger than the temperature increase (about 15 degrees or 30 degrees) used for calculation of the thermo-elasto-plastic analysis by the static implicit solution FEM.

Next, the analysis device 100 calculates the mass matrix [ M ] and the damping matrix [ C ] of the balance equation represented by the above equation (1) using various data read from the input unit 110 (step S40).

Then, the analysis device 100 calculates the displacement of each node by providing the load generated based on the temperature increase Δ T as a load vector of expression (1) and solving expression (1) by a dynamic explicit solution FEM (step S50). When the displacement is calculated, the analysis device 100 calculates the stress from the calculated displacement using various data read from the input unit 110 (step S60).

Next, the analysis device 100 determines whether or not the calculated displacement reaches a static equilibrium state (step S70). If the displacement does not reach the static equilibrium state (step S70: NO), the analysis device 100 returns the process to step S50, advances the virtual time step, and recalculates the displacement of each node by the dynamic explicit solution FEM.

When it is determined in step S70 that the displacement has reached the static equilibrium state (step S70: yes), the analysis device 100 determines whether the calculation is completed in all the temperature steps (step S80). When it is determined that there is an uncalculated temperature step (step S80: no), the analysis device 100 returns the process to step S30, advances the temperature step and updates the temperature field (by the temperature increase Δ T).

When it is determined in step S80 that the calculations are completed in all the temperature steps (step S80: yes), the analysis device 100 determines whether heat is applied to all the blocks (step S90). When it is determined that there is a block that has not been supplied with heat (step S90: NO), the analysis device 100 increments the counter i (step S100), and returns the process to step S30. Thereby, the analysis device 100 changes the heat supply block and executes a series of processes of steps S30 to S80 again. Then, when it is determined in step S90 that heat has been applied to all blocks (step S90: YES), the process is shifted to the end, and the series of thermo-elastic-plastic analyses is ended.

Fig. 12 is a diagram showing the contraction amount of the analysis target (analysis model 10) when the temperature increase Δ T is changed. Fig. 12 shows, as an example, the amount of shrinkage in the Y direction at a certain X coordinate in the coordinate system shown in fig. 1.

Referring to fig. 12, the magnitude of the changed temperature increase Δ T has a relationship of Δ T1< Δ T2< Δ T3< Δ T4, and a temperature increase of 100 degrees or more is also provided at the minimum temperature increase Δ T1. When the temperature increase Δ T is increased, the shrinkage amount increases and fluctuates, and deterioration in calculation accuracy can be seen, but a temperature increase Δ T larger in value than the temperature increase (15 degrees, 30 degrees) used in the calculation of the thermo-elastic-plastic analysis by the static implicit method FEM can be provided, and shortening of the calculation time can be achieved.

Fig. 13 is a diagram showing the shrinkage of the analysis target (analysis model 10) in the case of using the instantaneous heat source model (surface heat source). In fig. 13, the vertical axis represents the contraction amount (central value) in the X direction, and the horizontal axis represents the equivalent heat supply ratio η, which is the ratio of the heat supply amount of the surface heat source to the heat supply amount of the moving heat source. That is, the curve represents the contraction amount when the heat supply amount of the surface heat source is changed based on the heat supply amount of the moving heat source corresponding to the actual heat source.

Referring to fig. 13, in the present example, when the equivalent heat supply ratio η is η 0, the amount of contraction by the surface heat source is equal to the amount of contraction by the moving heat source. Therefore, in the analysis method according to the present embodiment, when each block is heated by a surface heat source, an instantaneous heat source model (surface heat source) having a heat supply amount adjusted with respect to the heat supply amount in the case of using a moving heat source (corresponding to actual heating) using η 0 as the correction coefficient shown in the above equation (2) is used.

As described above, in the present embodiment, the thermo-elasto-plastic analysis by the idealized explicit solver FEM is performed. Also, a large temperature increase (large temperature increase) is provided compared with the size of the temperature increase used in the thermo-elasto-plastic analysis by the static implicit method FEM. This can reduce the number of calculations and shorten the calculation time. In addition, according to the present embodiment, in the heating mode in which a plurality of blocks that are not adjacent to each other are simultaneously heated, the calculation time (simultaneous heating mode) can be shortened because the heating is performed for each of the plurality of blocks. Further, according to the present embodiment, since the heating for each block is performed by the surface heat source after the heating amount is adjusted, this point can also shorten the calculation time (instantaneous heat source model). Thus, according to the analysis method and the analysis apparatus according to the embodiments of the present disclosure, the calculation time can be significantly shortened.

[ modified examples ]

In the above-described embodiment, it is assumed that the calculation time required for performing the analysis is shortened by using the "large temperature increase" and the "instantaneous heat source model" described above and also using the "simultaneous heating mode" in the thermo-elasto-plastic analysis by the idealized explicit solution FEM. In the present modification, the calculation method itself of the idealized explicit solution FEM is further improved. This can further shorten the calculation time required for analysis.

The ideal explicit solution FEM is a method for improving the calculation efficiency for the thermo-elasto-plastic analysis based on the dynamic explicit solution FEM, and is a method capable of analyzing at high speed and with a memory saving, with the same analysis accuracy as the static implicit solution FEM generally used in the thermo-elasto-plastic analysis. However, in the ideal explicit solver FEM, the overall static imbalance force vector, i.e., the residual force vector, needs to be calculated in time steps in its calculation process. This calculation occupies most of the calculation time in the idealized explicit solution FEM, since it requires integral calculation of all the elements of equation (2) shown below.

[ number 2]

Here, { R } denotes the overall residual force vector, { F } denotes the load vector, [ B ]_e]Displacement-strain relationship matrix, σ, representing element e_eDenotes the stress vector of element e. In addition, Ne represents the number of elements of the analysis model. In the linear elasticity analysis, the integral calculation of the equation (2) is expressed by the following equation (3).

[ number 3]

Here, [ K ]_e]Rigid matrix representing element e, { u_eDenotes the displacement vector of element e. In the equation (3), since the integral calculation of the equation (2) is expressed by the product of the matrix and the vector, the calculation amount when the residual force vector is calculated by the equation (3) is overwhelmingly smaller than the calculation amount by the equation (2). Therefore, it is considered that in the idealized explicit solution FEM, the calculation amount can be significantly reduced by using the formula (3) in the calculation of the residual force vector, and the speed can be increased.

However, since the formula (3) is a calculation formula assuming a linear elastic body, it cannot be used directly in a nonlinear thermo-elasto-plastic analysis. Therefore, in the present modification, the formula (3) can be used also in the nonlinear elasto-plastic analysis by the idealized explicit solution FEM by a method shown in a flowchart to be described later.

In summary, first, as in the case of a general idealized explicit solver FEM, the displacement is calculated by performing time-step calculation N times based on the dynamic explicit solver FEM. In this case, the residual force at each time step is calculated using equation (3), and the calculation time can be shortened. After the calculation of the time step N times is completed, a nonlinear residual force vector is calculated using equation (2) and set as a load (external force). After that, the calculation of the time step is performed N times with the residual force vector as the load vector, and the displacement is calculated again. By repeating such a calculation process until the entire convergence is obtained, the number of times of calculation of the nonlinear residual force (expression (2)) can be significantly reduced, and an analysis result equivalent to that in the case of using expression (2) can be obtained.

Fig. 14 is a flowchart for explaining a processing procedure of FEM thermo-elastic-plastic analysis performed by the analysis device 100 in the present modification. This flowchart corresponds to fig. 11 described in the above embodiment.

Referring to fig. 14, the analysis device 100 executes the processing of steps S110 to S130. The processing performed in steps S110 to S130 is the same as the processing performed in steps S10 to S30 shown in fig. 11, and therefore, the description thereof will not be repeated.

When the temperature field is updated in step S130, the analysis device 100 calculates the rigidity matrix [ K ] using various data read from the input unit 110 (fig. 9)_e]Quality matrix [ M ]]And a damping matrix [ C ]](step S140). The analysis device 100 sets an initial value 1 to the counter t of the time step (step S150).

Next, the analysis device 100 provides the load generated from the temperature increase Δ T as the load vector { F } of equation (3), and calculates the residual force vector { R } using equation (3) based on the dynamic explicit solution FEM (step S160). Then, the analysis device 100 determines whether or not the counter t exceeds N (N is a predetermined natural number) (step S170). If the counter t is N or less (step S170: "NO"), the counter t is incremented (step S180), and the process returns to step S160.

When it is determined in step S170 that counter t exceeds N (step S170: yes), analysis device 100 calculates the displacement and stress of each node (step S190). Then, the analysis device 100 calculates the nonlinear residual force vector { R } by the above equation (2) (step S200).

Next, the analysis device 100 determines whether the solution has converged (step S210). For example, when it is determined that the calculated displacement has reached a static equilibrium state, it is determined that the solution has converged. If the solution does not converge (step S210: no), analysis device 100 updates the load vector { F } with the residual force vector { R } calculated in step S200 (step S220), and returns the process to step S150.

When it is determined in step S210 that the solution has converged (step S210: yes), analysis device 100 proceeds to step S230. The processing executed in steps S230 to S250 is the same as the processing executed in steps S80 to S100 shown in fig. 11, and therefore, the description thereof will not be repeated.

According to this modification, the number of times of integral calculation of the residual force occupying the majority of the calculation time of the idealized explicit solution FEM can be reduced, and therefore the calculation time required for analysis can be further shortened.

[ embodiment 2]

Based on the analysis results by the analysis method according to the above embodiment, a method for manufacturing a layered structure is shown in embodiment 2.

The present inventors performed analyses of residual stress and strain generated in a layered structure under various manufacturing conditions by using the above-described analysis method. As a result, the present inventors have obtained the following findings: when the surface layer of the shaped object is heated, when the peripheral edge-most block is heated and then the inner peripheral side block (for example, the inner side of one or two rows of the peripheral edge-most block) is heated, the residual stress of the peripheral edge-most portion, which most easily causes defects (cracks, deformation, etc.) due to the residual stress, is reduced. The reason why the residual stress in the outermost peripheral portion can be reduced by such a heating mode is considered to be that the residual stress in the stretching direction generated in the outermost peripheral portion block is reduced by the contraction of the block on the inner peripheral side of the outermost peripheral portion block as it melts and solidifies.

Fig. 15 is a diagram schematically showing a configuration of a metal 3D printer shown as an example of a manufacturing apparatus for a layered shaped object. Referring to fig. 15, the metal 3D printer includes a workpiece unit 300 and a controller 320. The workpiece portion 300 includes the elevator 20, the material feed device 310, the knife roll 28, the torch 30, and the laser 32. The elevator 20, knife roll 28, torch 30, and laser 32 are as illustrated in fig. 3, 4. The material supply device 310 supplies the metal powder 26 onto the intermediate shaped object 24.

The controller 320 includes a CPU, a RAM, a ROM, and input and output buffers (all not shown) for inputting and outputting various signals. The CPU expands and executes the program stored in the ROM in the RAM or the like. The program stored in the ROM is a program describing a processing procedure of the controller 320. The controller 320 executes control of each device in the workpiece section 300 in accordance with these programs. The control is not limited to the processing by software, and may be performed by dedicated hardware (electronic circuit).

As a main process executed by the controller 320, the controller 320 divides the uppermost layer of the intermediate shaped object 24 into a plurality of blocks, and controls the movement of the heat source (the torch 30 and the laser 32) so as to melt and solidify the metal powder 26 for each block. In each block, as shown in fig. 7, the controller 320 heats the surface of each block while moving the heat source (torch 30 and laser 32).

In the heating sequence of the plurality of blocks, the controller 320 controls the movement of the heat source (the torch 30 and the laser beam 32) so as to heat the block on the outermost periphery (hereinafter, referred to as a "first block group") of the plurality of blocks and then heat the block on the inner periphery (hereinafter, referred to as a "second block group"). The second block group may be on the inner periphery side of one row of the first block group, or on the inner periphery side of two or more rows of the first block group if the plurality of blocks are sufficiently subdivided.

Fig. 16 and 17 are diagrams for explaining an example of a heating procedure (heating mode) of a plurality of blocks. Referring to fig. 16 and 17, in the present example, the uppermost layer of the intermediate shaped object 24 is divided into 10 × 10 blocks. After the heating of the first block group at the outermost peripheral edge is completed (fig. 16), the second block group is heated (fig. 17). In these figures, it is not shown whether or not heating of each block on the inner peripheral side of the second block group is performed.

The heating order of the first block group and the second block group may be such that the blocks other than the second block group are heated in a random or predetermined order, and after the heating of all the blocks of the first block group is completed, the remaining blocks including the second block group are heated in a random or predetermined order. Alternatively, the first block group may be collectively and sequentially heated, and then the second block group may be collectively and sequentially heated.

Fig. 18 and 19 are diagrams showing an example of the analysis result of the residual stress generated in the layered structure. Fig. 18 shows the distribution of the residual stress σ X (tensile direction) in the X direction generated after the heating of all the blocks is completed, and fig. 19 shows the distribution of the residual stress σ Y (tensile direction) in the Y direction.

As can be seen from fig. 18, by performing heating in the heating procedure (heating pattern) shown in fig. 16 and 17, the residual stress σ X (tensile direction) in the X direction can be relatively reduced at the outermost peripheral edge portion surrounded by the wire.

As can be seen from fig. 19, by performing heating in the heating procedure (heating pattern) shown in fig. 16 and 17, the residual stress σ Y (tensile direction) in the Y direction can be relatively reduced in the outermost peripheral portion surrounded by the wire.

Fig. 20 is a flowchart illustrating an example of a procedure of the process executed by the controller 320. The series of processes shown in the flowchart is for determining the heating order of the first block group and the second block group, and corresponds to the process executed in step IV shown in fig. 3.

Referring to fig. 20, the controller 320 controls the movement of the heat sources (torch 30 and laser beam 32) so as to heat any one of the unheated blocks other than the one row of inner blocks (second block group) at the outermost periphery (step S310). Then, when the heating of the block is completed, the controller 320 determines whether the heating of all the blocks of the most peripheral block (first block group) has been completed (step S320).

In the case where the heating of all the blocks of the first block group is not completed (step S320: NO), the controller 320 returns the process to step S310. Further, the heating order of the blocks by repeatedly performing step S310 may be random or regular.

Then, when it is determined in step S320 that the heating of all the blocks of the first block group is completed (step S320: YES), the controller 320 controls the movement of the heat source (torch 30 and laser 32) so as to heat any one of the remaining blocks (including the second block group) that are not heated (step S330). Then, when the heating of the block is completed, the controller 320 determines whether the heating of all the blocks has been completed (step S340).

In the case where the heating of all the blocks is not completed (step S340: NO), the controller 320 returns the process to step S330. Further, the heating order of the blocks by repeatedly performing step S330 may be random or regular. Then, when it is determined in step S340 that the heating of all the blocks has been completed (step S340: YES), the controller 320 shifts the process to the end.

As described above, according to embodiment 2, it is possible to suppress residual stress generated in the outermost peripheral edge portion of the layered shaped object.

In addition, although the above embodiments have been described with respect to the lamination model using the metal 3D printer, the application range of the present disclosure is not limited thereto, and the present disclosure also includes a lamination model using resin powder, a lamination model in which molten resin or metal melted by arc discharge is deposited, and the like.

It should be understood that all points of the embodiments disclosed herein are illustrative and not restrictive. The scope of the present invention is indicated by the claims, rather than by the description of the embodiments described above, and all changes that come within the meaning and range of equivalency of the claims are intended to be embraced therein.

Description of the reference numerals

10: analyzing the model; 12: a base plate; 20: an elevator; 22. 26: a metal powder; 24: an intermediate molding; 28: a knife roll; 30: a torch; 32: laser; 34: a melting tank; 36: a layer; 38: a heat-affected part; 40: a surface heat source; 100: an analysis device; 110: an input section; 120: an I/F section; 130: a CPU; 140: a RAM; 150: a ROM; 160: an output section; 210: a temperature distribution calculation unit; 220: a displacement and stress calculation unit; 230: a simplified calculation setting section; 300: a workpiece portion; 310: a material supply device; 320: a controller; A1-A4: an area; B1-B9: and (5) blocking.

Claims

1. A method of analyzing a layered shaped object, which is generated by solidifying and continuously stacking molten materials, for analyzing residual stress and deformation generated in the layered shaped object by a computer, comprising the steps of:

inputting data for performing a thermo-elasto-plastic analysis of the laminated molding using Finite Element Method (FEM); and

calculating residual stress and deformation occurring in the layered shaped object by performing the thermo-elasto-plastic analysis in accordance with time-series data of a temperature distribution occurring in the layered shaped object with the shaping of the layered shaped object,

wherein, in the step of calculating the residual stress and strain, when a temperature increase is given in accordance with the time-series data, the displacement and stress of the layered shaped object are calculated by a dynamic explicit solution FEM until a predetermined static equilibrium condition is reached, and when the displacement reaches the static equilibrium condition, the temperature increase is given again and the displacement and stress are calculated again,

the magnitude of the temperature increase is set to a value larger than the magnitude of the temperature increase used in the thermo-elasto-plastic analysis of the layered structure by the static implicit solution FEM,

the heating of the layered structure is performed by using an instantaneous surface heat source having a heat supply amount adjusted with respect to a heat supply amount in a case of heating by the moving heat source.

2. The method for analyzing a layered structure according to claim 1,

heating the layered shaped article is performed for each of the uppermost layers of the plurality of divided blocks of the layered shaped article,

the heating of each of the plurality of blocks is performed using the instantaneous surface heat source.

3. The method for analyzing a layered structure according to claim 2,

heating of the laminated molding is performed in a heating mode in which at least two blocks that are not adjacent to each other are simultaneously heated.

4. The method for analyzing a layered structure according to any one of claims 1 to 3, wherein,

the amount of heat supplied by the instantaneous surface heat source is adjusted relative to the amount of heat supplied when heating is performed by the movable heat source such that the amount of shrinkage of the layered shaped article is equal to the amount of shrinkage of the layered shaped article when heating is performed by the movable heat source.

5. The method for analyzing a layered structure according to any one of claims 1 to 3, wherein,

the material is a metal, and the material is,

the temperature increment is at least 100 degrees or more.

6. The method for analyzing a layered structure according to any one of claims 1 to 3, wherein,

the magnitude of the temperature increase is determined based on the mechanical melting temperature of the metal constituting the layered structure.

7. An analysis device for a layered shaped article, which analyzes residual stress and deformation generated in the layered shaped article by solidifying a molten material in a surface layer, comprising:

an input unit configured to input data for performing a thermo-elasto-plastic analysis of the layered structure using an FEM (finite element method); and

a calculation unit configured to: calculating residual stress and deformation occurring in the layered shaped object by performing the thermo-elasto-plastic analysis in accordance with time-series data of a temperature distribution occurring in the layered shaped object with the shaping of the layered shaped object,

wherein the calculation unit calculates the displacement and stress of the layered structure by using a dynamic explicit solution FEM until a predetermined static equilibrium condition is reached when the temperature increase according to the time-series data is supplied, and supplies the temperature increase again and calculates the displacement and stress again when the displacement reaches the static equilibrium condition,

8. The stacked molding analysis device according to claim 7,

9. The stacked molding analysis device according to claim 8,

10. A method of manufacturing a layered shaped article, the layered shaped article being produced by solidifying and continuously stacking molten materials, the method comprising:

determining a heating pattern when heating the uppermost layer of the layered structure based on an analysis result obtained by the analysis method according to claim 1; and

heating the layered structure is performed in accordance with the heating pattern.

11. A device for manufacturing a layered shaped article, the layered shaped article being produced by solidifying and continuously stacking molten materials, the device comprising:

a heating device configured to heat an uppermost layer of the layered structure; and

a control device configured to control the heating device,

wherein the control device determines a heating pattern when heating the uppermost layer of the layered shaped object based on an analysis result obtained by the analysis method according to claim 1,

the control device controls the heating device so that the layered molding is heated in the heating mode.